Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Explain solution for RD Sharma Class 12 Chapter 19 Definite Integrals Exercise 19.4 (a) Question 16 maths textbook solution.

Explain solution for  RD Sharma Class 12 Chapter 19 Definite Integrals Exercise 19.4 (a) Question 16 maths textbook solution.

Answers (1)

Answer : \int_{a}^{b} x f(x) d x=\frac{a+b}{2} \int_{a}^{b} f(x) d x

Given : f(a+b-x)=f(x) and prove that

\int_{a}^{b} x f(x)=\frac{a+b}{2} \int_{a}^{b} f(x) d x

Hint : You must know the formula of \int_{a}^{b} f(x) d x

Solution : I=\int_{a}^{b} x f(x) d x

\begin{aligned} &I=\int_{a}^{b}(a+b-x) f(a+b-x) d x\left(\int_{a}^{b} f(x) d x=\int_{a}^{b} f(a+b-x) d x\right) \\ &I=\int_{a}^{b}(a+b-x) f(x) d x[f(a+b-x)=f(x)] \\ &I=\int_{a}^{b}(a+b) f(x) d x-\int_{a}^{b} x f(x) d x \end{aligned}

\begin{aligned} &I=\int_{a}^{b}(a+b) f(x) d x-I \\ &2 I=(a+b) \int_{a}^{b} f(x) d x \\ &I=\frac{a+b}{2} \int_{a}^{b} f(x) d x \end{aligned}

\int_{a}^{b} x f(x) d x=\frac{a+b}{2} \int_{a}^{b} f(x) d x \text { (proved) }

Posted by

infoexpert23

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE 12th Result 2026 Date: Here’s what previous years’ trends indicate
anam-khan

CBSE Class 12th marks uploading for schools in West Asia starts from April 8
anam-khan

CBSE question papers QR codes part of 'internal systems'; board cautions 'unverified claims'

Latest Question